OK, let's crack this. We're given 769 and our task is to multiply it by 177. Essentially, we'll be adding 769 to itself 177 times.
Step 1: 0 + 769 = 769
Step 2: 769 + 769 = 1538
Step 3: 1538 + 769 = 2307
Step 4: 2307 + 769 = 3076
Step 5: 3076 + 769 = 3845
Step 6: 3845 + 769 = 4614
Step 7: 4614 + 769 = 5383
Step 8: 5383 + 769 = 6152
Step 9: 6152 + 769 = 6921
Step 10: 6921 + 769 = 7690
Step 11: 7690 + 769 = 8459
Step 12: 8459 + 769 = 9228
Step 13: 9228 + 769 = 9997
Step 14: 9997 + 769 = 10766
Step 15: 10766 + 769 = 11535
Step 16: 11535 + 769 = 12304
Step 17: 12304 + 769 = 13073
Step 18: 13073 + 769 = 13842
Step 19: 13842 + 769 = 14611
Step 20: 14611 + 769 = 15380
Step 21: 15380 + 769 = 16149
Step 22: 16149 + 769 = 16918
Step 23: 16918 + 769 = 17687
Step 24: 17687 + 769 = 18456
Step 25: 18456 + 769 = 19225
Step 26: 19225 + 769 = 19994
Step 27: 19994 + 769 = 20763
Step 28: 20763 + 769 = 21532
Step 29: 21532 + 769 = 22301
Step 30: 22301 + 769 = 23070
Step 31: 23070 + 769 = 23839
Step 32: 23839 + 769 = 24608
Step 33: 24608 + 769 = 25377
Step 34: 25377 + 769 = 26146
Step 35: 26146 + 769 = 26915
Step 36: 26915 + 769 = 27684
Step 37: 27684 + 769 = 28453
Step 38: 28453 + 769 = 29222
Step 39: 29222 + 769 = 29991
Step 40: 29991 + 769 = 30760
Step 41: 30760 + 769 = 31529
Step 42: 31529 + 769 = 32298
Step 43: 32298 + 769 = 33067
Step 44: 33067 + 769 = 33836
Step 45: 33836 + 769 = 34605
Step 46: 34605 + 769 = 35374
Step 47: 35374 + 769 = 36143
Step 48: 36143 + 769 = 36912
Step 49: 36912 + 769 = 37681
Step 50: 37681 + 769 = 38450
Step 51: 38450 + 769 = 39219
Step 52: 39219 + 769 = 39988
Step 53: 39988 + 769 = 40757
Step 54: 40757 + 769 = 41526
Step 55: 41526 + 769 = 42295
Step 56: 42295 + 769 = 43064
Step 57: 43064 + 769 = 43833
Step 58: 43833 + 769 = 44602
Step 59: 44602 + 769 = 45371
Step 60: 45371 + 769 = 46140
Step 61: 46140 + 769 = 46909
Step 62: 46909 + 769 = 47678
Step 63: 47678 + 769 = 48447
Step 64: 48447 + 769 = 49216
Step 65: 49216 + 769 = 49985
Step 66: 49985 + 769 = 50754
Step 67: 50754 + 769 = 51523
Step 68: 51523 + 769 = 52292
Step 69: 52292 + 769 = 53061
Step 70: 53061 + 769 = 53830
Step 71: 53830 + 769 = 54599
Step 72: 54599 + 769 = 55368
Step 73: 55368 + 769 = 56137
Step 74: 56137 + 769 = 56906
Step 75: 56906 + 769 = 57675
Step 76: 57675 + 769 = 58444
Step 77: 58444 + 769 = 59213
Step 78: 59213 + 769 = 59982
Step 79: 59982 + 769 = 60751
Step 80: 60751 + 769 = 61520
Step 81: 61520 + 769 = 62289
Step 82: 62289 + 769 = 63058
Step 83: 63058 + 769 = 63827
Step 84: 63827 + 769 = 64596
Step 85: 64596 + 769 = 65365
Step 86: 65365 + 769 = 66134
Step 87: 66134 + 769 = 66903
Step 88: 66903 + 769 = 67672
Step 89: 67672 + 769 = 68441
Step 90: 68441 + 769 = 69210
Step 91: 69210 + 769 = 69979
Step 92: 69979 + 769 = 70748
Step 93: 70748 + 769 = 71517
Step 94: 71517 + 769 = 72286
Step 95: 72286 + 769 = 73055
Step 96: 73055 + 769 = 73824
Step 97: 73824 + 769 = 74593
Step 98: 74593 + 769 = 75362
Step 99: 75362 + 769 = 76131
Step 100: 76131 + 769 = 76900
Step 101: 76900 + 769 = 77669
Step 102: 77669 + 769 = 78438
Step 103: 78438 + 769 = 79207
Step 104: 79207 + 769 = 79976
Step 105: 79976 + 769 = 80745
Step 106: 80745 + 769 = 81514
Step 107: 81514 + 769 = 82283
Step 108: 82283 + 769 = 83052
Step 109: 83052 + 769 = 83821
Step 110: 83821 + 769 = 84590
Step 111: 84590 + 769 = 85359
Step 112: 85359 + 769 = 86128
Step 113: 86128 + 769 = 86897
Step 114: 86897 + 769 = 87666
Step 115: 87666 + 769 = 88435
Step 116: 88435 + 769 = 89204
Step 117: 89204 + 769 = 89973
Step 118: 89973 + 769 = 90742
Step 119: 90742 + 769 = 91511
Step 120: 91511 + 769 = 92280
Step 121: 92280 + 769 = 93049
Step 122: 93049 + 769 = 93818
Step 123: 93818 + 769 = 94587
Step 124: 94587 + 769 = 95356
Step 125: 95356 + 769 = 96125
Step 126: 96125 + 769 = 96894
Step 127: 96894 + 769 = 97663
Step 128: 97663 + 769 = 98432
Step 129: 98432 + 769 = 99201
Step 130: 99201 + 769 = 99970
Step 131: 99970 + 769 = 100739
Step 132: 100739 + 769 = 101508
Step 133: 101508 + 769 = 102277
Step 134: 102277 + 769 = 103046
Step 135: 103046 + 769 = 103815
Step 136: 103815 + 769 = 104584
Step 137: 104584 + 769 = 105353
Step 138: 105353 + 769 = 106122
Step 139: 106122 + 769 = 106891
Step 140: 106891 + 769 = 107660
Step 141: 107660 + 769 = 108429
Step 142: 108429 + 769 = 109198
Step 143: 109198 + 769 = 109967
Step 144: 109967 + 769 = 110736
Step 145: 110736 + 769 = 111505
Step 146: 111505 + 769 = 112274
Step 147: 112274 + 769 = 113043
Step 148: 113043 + 769 = 113812
Step 149: 113812 + 769 = 114581
Step 150: 114581 + 769 = 115350
Step 151: 115350 + 769 = 116119
Step 152: 116119 + 769 = 116888
Step 153: 116888 + 769 = 117657
Step 154: 117657 + 769 = 118426
Step 155: 118426 + 769 = 119195
Step 156: 119195 + 769 = 119964
Step 157: 119964 + 769 = 120733
Step 158: 120733 + 769 = 121502
Step 159: 121502 + 769 = 122271
Step 160: 122271 + 769 = 123040
Step 161: 123040 + 769 = 123809
Step 162: 123809 + 769 = 124578
Step 163: 124578 + 769 = 125347
Step 164: 125347 + 769 = 126116
Step 165: 126116 + 769 = 126885
Step 166: 126885 + 769 = 127654
Step 167: 127654 + 769 = 128423
Step 168: 128423 + 769 = 129192
Step 169: 129192 + 769 = 129961
Step 170: 129961 + 769 = 130730
Step 171: 130730 + 769 = 131499
Step 172: 131499 + 769 = 132268
Step 173: 132268 + 769 = 133037
Step 174: 133037 + 769 = 133806
Step 175: 133806 + 769 = 134575
Step 176: 134575 + 769 = 135344
Step 177: 135344 + 769 = 136113

So, 769*177 = 136113